Homological mirror symmetry for punctured spheres

Abstract

We prove that the wrapped Fukaya category of a punctured sphere ($S^2$ with an arbitrary number of points removed) is equivalent to the triangulated category of singularities of a mirror Landau-Ginzburg model, proving one side of the homological mirror symmetry conjecture in this case. By investigating fractional gradings on these categories, we conclude that cyclic covers on the symplectic side are mirror to orbifold quotients of the Landau-Ginzburg model.

38 pages, 5 figures; v2: minor revisions (similar to published version)

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Cited by in corpus (3)

• Finite group actions on Lagrangian Floer theory
• HMS for punctured tori and categorical mapping class group actions
• The A-infinity algebra of an Elliptic Curve and the j-invariant